Conformally invariant random planar objects
By: Stephane Benoist
Publisher: [publisher not identified]
Published: 2016
Place of publication: [New York, N.Y.?]
Language: eng
Description: This thesis explores different aspects of a surprising field of research: the conformally invariant scaling limits of planar statistical mechanics models. The aspects developed here include the proof of convergence of certain interfaces in the critical Ising magnetization model (joint work with Hugo Duminil-Copin and Clement Hongler), a study of the near-critical behavior of the uniform spanning tree in the scaling limit (joint work with Laure Dumaz and Wendelin Werner), the construction of an interesting measure on continuous loops satisfying a certain stability property under deformation (joint work with Julien Dubedat) as well as some related algebraic considerations, and finally, notes on a paper of Sheffield, that studies a certain coupling of the scaling limits of discrete interfaces - SLE curves - together with random surfaces obtained from the Gaussian free field.
Notes: Department: Mathematics.

Thesis advisor: Julien Dubedat.

Thesis (Ph.D.)--Columbia University, 2016.